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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
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u.
rali
Deseementis hyperboliers, conuexis s concanis.
PROPOSTTI
Rea lyperbolae terminacie, criangulum maximum inlexibere.
Constructio es demonstratio.
crum D, cerminetur rectâ
AC; qua divisa bitariam
in B, Ponatur diaeTer DF., Oc.
currens sectioni in B. de iunsantur
AB, C B, dico crianoulum ABC.
cnemaximum illorum, que hyper-
bola AB C inscribi postunE. Pona-
cur per B concingens F. B. 2 aequi-
dictabit illa rectae AC: ducatuE
dein quaenis H C, paraIlela BF,
occurrens lectioni in G. Pacec C punctum esse infra lineam EB, adeoque, GFI
minorem B F. vndecriangulum AC: C minus est criangulo A BC: crionpulum igi-
cuT AB C maximum cA. daca isicur hyperbolx terminaca, etc. Quoderactacien.
dum.
IIdempositis:
P R OP OSIFIO CTI
LDico ABC criangulum maiusesle dimidio tesmenei AB C.
Demonstratio.
GRiBEnEUE Ex A de C Eguidistantes BF, OCCUTeNEES FB concingenti in F e
K. quoniam isicur ram AB C triarigulum, quam b F. P. parallelogeammum, du- menin.
Excle
plum est crianguli AB F sequalia lunc parallelogrammum F F, de criangulum ABC
vndo J.C parallelogrammum duplum est crianguli AB C: sed F C parallelo-
sxammum maius est segmento AB C, (cum F K contingens tora cadat extra lectio-
nem,) criangulum isicut AB C. dimidium parallelogrammi F C, maius quoque est
dimidio lesmenti ABC. QuodCtat demonctrandum.
Cdronarium.
1
Zperbola ABC, cuius con-
Inc exparecracio ntcribendi ctianoulum cuiuis segmenco hyperbolico, quod
licatis; consticuendo scilicer rectani aliquam OHI, qua ad BF, datam rationem
obcineat; si enim ad C deducancur rectae AC, C C, criangulum AC C ad AB C,
elt in racione linca 6FI. 3d BP: cum bales sINECOMMUHCS.
Sct. F 5. L1 53 CBL S. 3CMI
2A. I Bupou el
Eil arspis
aan. Cdi 1244C4
damaia ccaticlum lletcu dalatutabene cachilela talhotis inaequa
stcP
11II